![Copy content]()
gp:[N,k,chi] = [12,22,Mod(1,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
Newform invariants
![Copy content]()
sage:traces = [2]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
![Copy content]()
gp:f = lf[1] \\ Warning: the index may be different
![Copy content]()
sage:f.q_expansion() # note that sage often uses an isomorphic number field
![Copy content]()
gp:mfcoefs(f, 20)
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2880\sqrt{3190177}\).
We also show the integral \(q\)-expansion of the trace form.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
![Copy content]()
gp:mfembed(f)
| \( p \) |
Sign
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( +1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} - 28827900T_{5} - 453753148117500 \)
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(12))\).
![Copy content]()
![Toggle raw display]()
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( (T + 59049)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{2} + \cdots - 453753148117500 \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} + \cdots - 10\!\cdots\!04 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} + \cdots + 11\!\cdots\!36 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + \cdots + 13\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + \cdots - 98\!\cdots\!44 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} + \cdots + 22\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} + \cdots - 11\!\cdots\!04 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots - 68\!\cdots\!24 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots + 85\!\cdots\!76 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots - 10\!\cdots\!36 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots + 30\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots + 15\!\cdots\!76 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots + 98\!\cdots\!16 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots + 81\!\cdots\!44 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots - 88\!\cdots\!64 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots + 75\!\cdots\!84 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots - 37\!\cdots\!24 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 77\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots - 77\!\cdots\!16 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots - 86\!\cdots\!96 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots + 25\!\cdots\!96 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots + 96\!\cdots\!00 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots + 34\!\cdots\!64 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
